Geometric Invariant Theory, Volume 34

Front Cover
Springer Science & Business Media, 1994 - Mathematics - 292 pages
1 Review
"Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.
 

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Contents

I
1
II
2
III
4
IV
9
V
13
VI
19
VII
24
VIII
27
XXVIII
115
XXX
120
XXXI
124
XXXII
127
XXXIII
129
XXXIV
138
XXXV
142
XXXVI
144

IX
30
X
36
XI
44
XII
48
XIII
55
XIV
63
XV
67
XVI
72
XVII
76
XIX
79
XX
83
XXI
86
XXII
88
XXIII
89
XXIV
96
XXV
98
XXVI
104
XXVII
109
XXXVIII
148
XXXIX
152
XL
156
XLI
160
XLII
164
XLIII
172
XLIV
181
XLV
185
XLVI
191
XLVII
202
XLVIII
205
XLIX
206
L
217
LI
234
LII
253
LIII
291
Copyright

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Loop Groups
Andrew Pressley,Graeme Segal
No preview available - 1988
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About the author (1994)

Biography of  David Mumford

David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics.

Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.

Kirwan, Mathematical Institute, University of Oxford.